In this article, we introduce the recently developed intrinsic estimator method in the age‐period‐cohort (APC) models in examining disease incidence and mortality data, further develop a likelihood ratio (L‐R) test for testing differences in temporal trends across populations, and apply the methods to examining temporal trends in the age, period or calendar time, and birth cohort of the US heart disease mortality across racial and sex groups. The temporal trends are estimated with the intrinsic estimator method to address the model identification problem, in which multiple sets of parameter estimates yield the same fitted values for a given dataset, making it difficult to conduct comparison of and hypothesis testing on the temporal trends in the age, period, and cohort across populations. We employ a penalized profile log‐likelihood approach in developing the L‐R test to deal with the issues of multiple estimators and the diverging number of model parameters. The identification problem also induces overparametrization of the APC model, which requires a correction of the degree of freedom of the L‐R test. Monte Carlo simulation studies demonstrate that the L‐R test performs well in the Type I error calculation and is powerful to detect differences in the age or period trends. The L‐R test further reveals disparities of heart disease mortality among the US populations and between the US and Japanese populations.

中文翻译：

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年龄-周期-队列模型时间趋势的似然比检验，应用于美国人口心脏病死亡率差异以及与日本的比较

在本文中，我们介绍了最近开发的年龄-周期-队列（APC）模型中用于检查疾病发病率和死亡率数据的内在估计方法，进一步开发了似然比（L-R）检验来测试不同人群的时间趋势差异，并应用这些方法来检查不同种族和性别群体中美国心脏病死亡率的年龄、时期或日历时间以及出生队列的时间趋势。使用内在估计器方法来估计时间趋势，以解决模型识别问题，其中多组参数估计对给定数据集产生相同的拟合值，使得难以对时间趋势进行比较和假设检验不同人群的年龄、时期和队列。我们在开发 L-R 测试时采用惩罚剖面对数似然方法来处理多个估计量和模型参数数量不同的问题。辨识问题还导致APC模型的过度参数化，需要对L-R检验的自由度进行修正。蒙特卡罗模拟研究表明，L-R 检验在 I 类误差计算中表现良好，并且能够有效检测年龄或周期趋势的差异。L-R 检验进一步揭示了美国人群以及美国和日本人群之间心脏病死亡率的差异。